Modularity of $\operatorname{PGL}_2(\mathbb{F}_p)$-representations over totally real fields
| Autor: | Allen, Patrick B., Khare, Chandrashekhar B., Thorne, Jack A. |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Proc. Natl. Acad. Sci. USA 118 (2021), no. 33, e2108064118 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1073/pnas.2108064118 |
| Popis: | We study an analogue of Serre's modularity conjecture for projective representations $\overline{\rho}: \operatorname{Gal}(\overline{K} / K) \rightarrow \operatorname{PGL}_2(k)$, where $K$ is a totally real number field. We prove new cases of this conjecture when $k = \mathbb{F}_5$ by using the automorphy lifting theorems over CM fields established in previous work of the authors. Comment: 11 pages. Refereed version |
| Databáze: | arXiv |
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